White muscle strain in the common carp and red to white muscle gearing ratios in fish

Fish are good animals for modelling studies on locomotion because of the anatomical separation of their red and white muscle fibres. Fish fast-starts are powered predominantly by the white muscle, which is composed of fast-twitch fibres (Rome et al., 1988; Altringham and Johnston, 1988; van Leeuwen et al., 1990; Jayne and Lauder, 1993), and are used for both prey capture and escape manoeuvres. These motions provide a stereotypical behaviour in which the myotomal muscles work near to their maximal performance, and they have been the subject of many studies (for a review, see Domenici and Blake, 1997).

Red myotomal muscle fibres in most fish are arranged parallel to the longitudinal axis of the body in one or more superficial bands. In contrast, the white fibres that constitute the bulk of the musculature follow complex helical trajectories in successive myotomes and are orientated at angles of up to 40 ° to the longitudinal axis of the fish (Alexander, 1969; Kashin and Smolyaninov, 1969). Two main patterns of white fibre orientation have been described, one of which is restricted to selechians and teleosts with primitive taxonomic features such as Anguilla and Salmo (Alexander, 1969). In the majority of teleost families, the white fibres are arranged in coaxial bundles following geodesic paths around spaces that are cylindrical when the trunk is held straight and that change to arcs of toroids during bending. Alexander (1969) proposed that this complex helical arrangement enabled all the white fibres in a cross section to contract to a similar extent when the body bends.

Muscles do work by shortening while actively producing force. The power output of muscle fibres under conditions simulating swimming behaviour can be determined provided that the strain and stimulation patterns are both accurately known (Josephson, 1985; Altringham and Johnston, 1990; Altringham et al., 1993; Rome et al., 1993; Johnston et al., 1995). Briefly, the force generated by isolated muscle fibres is measured whilst those fibres are subjected to the strain and stimulation cycles determined during specific behaviours in vivo (James and Johnston, 1998; Wakeling and Johnston, 1998). The onset and duration of stimulation relative to the shortening cycle can be determined by electromyography (e.g. Jayne and Lauder, 1993).

Several approaches have been described in the literature for determining the white muscle fibre strain during swimming. Alexander (1969) modelled the complex muscle geometry during steady swimming and predicted that the white muscle fibres should contract with 0.2–0.3 of the strain of the red muscle fibres, i.e. with a mean gearing ratio of 4. The strain of red muscle fibres during continuous swimming has been estimated using beam theory on the digitised images of body shape taken using high-speed cinematography (Rome et al., 1988; van Leeuwen et al., 1990; van Leeuwen, 1992; Lieber et al., 1992; Johnston et al., 1995). The white muscle strains for these studies were subsequently determined using Alexander’s (1969) gearing ratio of 4 (Rome et al., 1988; van Leeuwen, 1992; Lieber et al., 1992) or a gearing ratio of 2 (van Leeuwen et al., 1990; Johnston et al., 1995; both studies using the same methods). Rome and Sosnicki (1991) used histology and laser diffraction to measure the sarcomere length of muscle fibres from dead carp which had been allowed to set in rigor mortis whilst bent into shapes typical of swimming. They concluded that, during swimming, the white muscle fibres contracted with gearing ratios of between 1.6 and 4.3. More recently, the technique of sonomicrometry has been used to measure directly the strain of white muscle during fast-starts in several species (Covell et al., 1991; Franklin and Johnston, 1997; James and Johnston, 1998; Temple, 1998; Wakeling and Johnston, 1998). Pairs of piezoelectric devices are implanted into the muscle with an orientation parallel to the direction of shortening. These sonomicrometry crystals emit and receive ultrasonic pulses enabling the gap between them to be estimated from the transit time of each pulse. Unfortunately, the sonomicrometry technique is only applicable to superficial layers of white muscle fibres which have similar orientations to the red fibres. In the present study on fast-starts in the common carp (Cyprinus carpio), we have compared muscle strain estimates from sonomicrometry recordings and beam theory and investigated the possibility that the strains obtained are a function of the chordwise distance of the fibres from the spine. The model of muscle fibre geometry proposed by Alexander (1969) was used to estimate the strain of deeper layers of white muscle fibre using values of body curvature obtained from ciné films of fast-starts. These results were compared with those from a quicker approach to estimating strain based on the position of the centroid of white fibre cross-sectional area.

Common carp Cyprinus carpio L. were supplied by Humberside Fisheries, Driffield, UK. The fish were kept in an outdoor tank for 2 months between November 1997 and January 1998, during which time the mean daily water temperature dropped with ambient temperature from 11 to 4 °C. Fish were fed regularly with carp pellets and bloodworm.

Hooks were made from 0.125 mm stainless-steel wire, coated with a thin film of Perspex and then bonded to Triton Technology VD5-2 sonomicrometry crystals using epoxy resin. The barb on each hook served both to loop into the end of a hypodermic needle for inserting the crystal into the muscle and to maintain the crystal’s subsequent position within it.

Anaesthesia was initiated with a 1:5000 (w/v) solution of bicarbonate-buffered MS222 (ethyl m-aminobenzoate) and maintained during surgery with a 1:3 dilution of the above solution. Surgery was performed at the ambient temperature of the fish’s holding tank. Pairs of crystals were implanted vertically into the rostral muscle at a depth of 5 mm and with approximately 7 mm separation. Single pairs of crystals were implanted into six carp of total length approximately 150 mm. The crystals were located 0.43L from the snout and 0.54b from the sagittal plane, where L and b are fish total length and half the local chord (width) respectively. Two pairs of crystals were additionally implanted on the right side of a 385 mm C. carpio at a longitudinal position of 0.41L and chordwise positions of 0.32b and 0.80b.

Wires from all the crystals were sutured to the front of the dorsal fin, allowing enough slack for the body to bend without the crystal position being disturbed. Precise crystal position was confirmed by post mortem dissection. Errors in strain measurements introduced due to crystal misalignment were less than 0.3 %, and the crystal lens error was less than 0.5 % (Sonomicrometer 120 operating manual, Triton Technology Inc. USA): both these sources of error were therefore ignored. Analogue signals from the Triton Technology 120 sonomicrometer were read into a personal computer via a National Instruments DAQPad-MIO-16XE-50 data-acquisition card. Strain data were sampled in a LabView (National Instruments) environment at 1 kHz. Event signals generated by the computer synchronized the strain data to the event light within the ciné camera.

The six 150 mm carp were swum in a static tank 400 mm×300 mm×100 mm (length×width×depth). Water temperature was the ambient temperature of the day. Fast-starts were elicited by thrusting a rod towards the snout of the fish, which was initially positioned in the centre of the tank. In most cases, the fish moved without making contact with the rod. A recovery period of at least 15 min was allowed between starts. A relatively small filming tank was required because of the finite length of the sonomicrometry cables attached to the fish. This study considered only the relationship between body bending and measured sonomicrometry strain, and so edge effects were ignored. The 385 mm carp was swum in a circular tank of 750 mm diameter and 400 mm depth; this fish was not filmed.

Even illumination for the tank was provided by a 250 W bulb focused onto a frosted sheet beneath it. Fast-starts were filmed on 16 mm Ilford HP5 film using a Nac Inc., Japan, E-10 high-speed ciné camera at 500 frames s⁻¹ using a 100 mm lens at an aperture of f5.6. Overhead silhouette images were obtained by filming via a mirror set at 45 °. The light path between the film and the fish was 2.6 m, and the frame diagonal was approximately four fish lengths long. Timing for the sequences was calibrated by a light strobing at 100 s⁻¹ within the camera. A second internal light was used to synchronise the films to the sonomicrometry data read into a computer. Sequences were digitized on a NAC 160F film motion image analyzer. The standard error of digitizing a fixed point on sequential frames corresponded to 0.001L.

The strain of white muscle fibres parallel to the spine can be predicted in a similar manner to ε_red if the chordwise distance b′ between the spine and that fibre is known. We hypothesized that superficial white muscle strain, as measured using the sonomicrometry technique, is the same as the strain that can be calculated for those fibres from the body shape. This hypothesis was tested in two ways. First, the superficial muscle strain measured using the sonomicrometry crystals was compared with the strain predicted from the spine curvature and the chordwise location of those crystals. The nullhypothesis is that these measured and modelled strains should be the same. This hypothesis was tested by taking a series of high-speed ciné sequences of fast-starting carp which were synchronised to sonomicrometry recordings from the superficial muscle fibres.

White fibre strain deep within the myotome is more complicated than simple bending theory would suggest. Theoretical considerations have shown that, when the deep myotomal muscle fibres are modelled as a complex array of helical trajectories, the muscle strain may be more uniform across a half-section of fish than that predicted by the radius of curvature and chordwise position of those fibres (Alexander, 1969). Such helical trajectories have been measured in many teleost species, and the strain of their fibres can be calculated from the change in length of a curve that runs helically around a cylinder in the straight fish case, but follows a geodesic path around an arc of a toroid when the fish bends (Alexander, 1969).

The strain of white muscle fibres running helical routes around cylindrical surfaces within fish has been calculated for typical steady-swimming motions with maximum spine curvatures of 1/10 (Alexander, 1969).In this study, we re-evaluated this helical fibre-trajectory model using the increased body flexures found during fish fast-starts. The initial parameters defining the geometry of the myotome were kept as Alexander’s (1969) original values, i.e. with ‘the pitch of the helices for the outermost trajectories lying between the values obtained from microscope sections of Xiphophorus and Hyphessobrycon’, and with helix axes lying 1/5 from the median plane. These values are typical for teleosts in general (as shown for Clupea, Gonichthys, Idus, Ciliata, Sebastes, Scomber and Pterophyllum); however, they are not representative for the more primitive selacian fish, Anguilla and Salmo (Alexander, 1969). Body curvatures during fast-starts are greater than for steady swimming, and so the model was tested for the curvature of 1/7.8 typical for C. carpio fast-starts at longitudinal positions between 0.5L and 0.7L and for the more extreme case of 1/5 that has been noted for some fish (Alexander, 1969).

White muscle strains from this model were evaluated using Mathematica version 3.0 software, Wolfram Research Inc. Red muscle strains and gearing ratios for these body flexures were calculated using equations 4 and 6. Actual red muscle strain may differ from these estimates as a result of swelling of the muscles during contraction. However, when subsequently calculating white muscle strain using the gearing ratios from equation 6, these errors will cancel and thus can be ignored.

The white fibre distribution was determined for the six 150 mm C. carpio used for the fast-start experiments and for an additional eight C. carpio ranging in total length from 46 to 400 mm. The fish were frozen post mortem and then partially thawed before being sectioned. Each fish was divided into 10 equal-thickness transverse sections. Images of the sections were grabbed into a Macintosh computer via a JVC TK-1281 video camera with a 135 mm focal length lens. Outlines of the sections were digitized using NIH Image version 1.24 software, and the maximum chord and the chordwise distance from the spine to the centroid of white muscle area for each half-section were measured.

The first null hypothesis was accepted if a two-tailed t-test showed no significant difference between unity and the slope of the reduced major axis regression between strain measured using sonomicrometry and strain calculated from body shape. The second hypothesis was tested by comparing the slope of the linear regression through the measured strains from the far 0.8b set of sonomicrometry crystals against that for the near 0.32b crystals. This regression was calculated using a reduced major axis technique. This slope was compared with the ratio of the chordwise distance of the pairs of crystals from the sagittal plane using a two-tailed t-test: a match between the values leads to an acceptance of the null hypothesis.

Statistical differences (t-tests) were accepted at 95 % confidence levels. The regression between λ and î, where î is the length-specific longitudinal distance from the snout, was calculated using simple polynomial regression techniques (Zar, 1996). Values are presented as means ± S.E.M.

Fifty-four synchronized sonomicrometry and high-speed ciné sequences were obtained for the six 150 mm individuals. From these, 23 recordings were analyzable for both techniques. These carp had a mean total length L of 148.9±4.4 mm. The centre of each pair of sonomicrometry crystals was placed 0.431±0.016L from the snout and 0.040±0.002L from the spine. The mean length-specific half-width of the fish at this location was 0.075±0.003L. Representative white muscle strains measured using sonomicrometry and also calculated from the body curvature using a gearing ratio of 2 are shown for fast-starts in Fig. 1.

Fish typically began their fast-starts from a straight position, and data were recorded from the first complete cycle of body bending and muscle length changes. The first hypothesis was tested by comparing the measured sonomicrometry strain for these starts with the strain predicted using equations 2 and 3 and the chordwise position of the crystals. Data were recorded for the initial strain, the final strain and the peak values from the first cycle, and these are shown in Fig. 2. The slope of the reduced major axis regression through these data (1.225±0.367) is not significantly different from unity. Therefore, we must accept the hypothesis that sonomicrometry strain from these muscle fibres is not significantly different from the strain predicted using simple bending beam theory.

Strains were measured using sonomicrometry from the two crystal positions for 16 fast-starts for the 385 mm carp. For each start, discrete pairs of strains were measured at the beginning and end of the first body bending cycle, and the peak values and the median value were also measured (Fig. 3). The reduced major axis regression through these data was:

White muscle strain calculated from the helical model of fibre geometry is dependent on the magnitude of spine curvature. Alexander (1969) predicted white muscle strains of 0.02–0.03 during steady swimming for a fish bending to a curvature ĉof 1/10⁠, corresponding to a red muscle strain of 0.10. During fast-starts, fish bend to tighter curvatures than for steady swimming, and so the model was tested at the tighter curvature of 1/7.8 appropriate to fast-starts in C. carpio. The resulting ε_w ranged between 0.026 and 0.053, with a red muscle strain of 0.128. Alexander (1969) acknowledged that during turning or accelerating the curvature can reach 1/5⁠. Reworking the model with this more extreme curvature of 1/5 resulted in values of ε_w ranging between 0.040 and 0.085, with a red muscle strain of 0.200.

Mean fish width decreased from its maximum at 0.3L towards the tail (Fig. 4). White myotomal muscle fibres occurred in rostral blocks at 0.2L, extended ventrally around the lower edge of the fish by 0.3L and occupied most of the body volume by 0.7L. Only two fish had muscle fibres extending as far as the section at 0.8L, so values for 0.8L are not given in Fig. 4.

Gearing ratios, calculated using simple bending theory from white fibre distribution, showed no significant systematic change with increasing body length for each longitudinal position tested. Thus, mean values for each position were pooled from all the fish (Fig. 5). Mean gearing ratios are also shown in Fig. 5 for the group of six (150 mm) fish from the fast-start study. These gearing ratios are approximately 2.0 between 0.2L and 0.4L, and then increase to 2.6 by 0.7L. The data are well represented by the least-squares cubic regression line:

In most teleost fish, the white myotomal muscle fibre trajectories can be described as longitudinal helices (Alexander, 1969). The fibres follow geodesic paths around cylindrical spaces in straight fish, but these spaces change to arcs of toroids during bending. A geometrical consequence of this arrangement is that white muscle strain is more uniform across a section than would be predicted by simple bending theory for fibres parallel to the spine (Alexander, 1969). We have shown in this study that the superficial white muscle strain measured using sonomicrometry crystals is not significantly different from the strain that would be predicted by simple bending theory and that this strain therefore varies with the chordwise position of those crystals. Hence, this measured strain will not necessarily equal the more uniform strain that is adopted by the majority of the deeper fibres.

These arguments explain some of the variance in gearing ratios found during fish fast-starts (Wakeling and Johnston, 1998). Gearing ratios for three species ranged between 2.07 and 2.49 for Notothenia rossii but were estimated at 4.09 for Notothenia coriiceps; these ratios were taken from sonomicrometry-based measurements as estimates of white muscle and red muscle strains calculated from the bending of the fish (equation 2). The predicted gearing ratio for these two closely related notothenioid species differed even though the body curvatures and red muscle strains were similar and the fish were swum at the same temperature, size and length-specific velocities (Wakeling and Johnston, 1998). This difference may be explained by the sonomicrometry crystals being positioned closer to the spine in N. coriiceps (Franklin and Johnston, 1997) than in N. rossii (Wakeling and Johnston, 1998). Thus, differences in experimental positioning of the sonomicrometry crystals may result in differences in the apparent white muscle strains even in fish swimming with similar kinematics and muscle dynamics.

If sonomicrometry measurements do not necessarily give representative estimates of the deep white muscle strain, then an alternative approach should be used. Strain can be estimated from the curvature of the spine, the local width of the fish and an appropriate gearing ratio (equations 3, 4 and 6). Such estimates give qualitatively similar results to direct sonomicrometry measurements of muscle strain (Fig. 1), and the variance of these estimates from sonomicrometry measurements (Fig. 2) is no greater than that for two adjacent sonomicrometry measurements (Fig. 3). However, the magnitude of these strain estimates is determined by the choice of gearing ratio, and there is little empirical evidence to suggest what the gearing ratios should be in teleost fish.

The position of the spine was assumed to lie equidistant between the two sides of the fish. This assumption has been tested using X-ray photographs and leads to smaller errors than when the spine is assumed to divide the muscle area equally between the two sides (Wakeling and Johnston, 1998). If the two sides of the fish change width as a result of the muscle bulging as it contracts, then the two sides of the fish would alternately become thicker and thinner by 0.0016L (data from Wakeling and Johnston, 1998). The muscle strains for these carp would therefore differ by 3 % from estimates based on an equidistant position for the spine. It is likely that such an error would be less than that introduced by the choice of gearing ratio.

A range of gearing ratios between 1.62 and 4.25 has been estimated from sarcomere length measurements in frozen sections of carp Cyprinus carpio which had previously been allowed to go into rigor whilst bent into different shapes (Rome and Sosnicki, 1991). Large accelerations are achieved during fast-starts because of high force production from the muscles. Indeed, work-loop experiments show that individual muscle fibres working under fast-start shortening regimes achieve forces that range between 53 % and 90 % of the maximum possible value during tetanic contractions (data from Franklin and Johnston, 1997; James and Johnston, 1998). However, it is unlikely that all the muscle fibres would simultaneously produce maximum force during swimming on either side of the body, let alone on both sides at once. The net maximum force production during fast-starts will thus be a fraction of that during rigor or tetanus. If a muscle in rigor produces an unnaturally high force, then it may stretch the tendons and connective tissues beyond the extent found during swimming, and this would result in muscle strain during rigor being smaller for a given curvature than would be found during fast-starts. Furthermore, only the fibres parallel to the longitudinal axis of the fish were measured in the frozen C. carpio (Rome and Sosnicki, 1991). These white fibres show smaller strains than oblique fibres in helical trajectories, again leading to an underestimation of mean muscle strain.

Gearing ratios quoted from the study of Alexander (1969) have been based implicitly on the ratio of the red fibre strain to the arithmetic mean of the white fibre strains (Rome et al., 1988). However, these estimates do not account for differences in the number of fibres contracting across the range of strains. Weighted-mean white fibre strains can be calculated using a weighting of fibre area, and these result in gearing ratio estimates of 3.66 for Alexander’s (1969) steady-swimming example, 2.80 for the fast-starting C. carpio in the present study and 2.74 for the more extreme case of fast-starting fish in general.

The model of helical fibre geometry is considered to be a reasonably accurate model for the main bundles of muscle fibres in the anterior caudal region of teleosts (Alexander, 1969). The gearing ratios estimated for this region are not significantly different from the gearing ratios predicted from the caudal muscle fibre distributions. In the anterior caudal region, there is a relatively uniform distribution of white muscle fibres across the fish. However, in more rostral regions, the abdominal cavity displaces much of the muscle towards the skin (Fig. 6). The mean white muscle strain in this rostral region is thus greater, and the gearing ratio is smaller than for the anterior caudal myotomes. Gearing ratio estimates based on the white fibre distribution similarly show this trend of a low value in the anterior region increasing to a maximum at the anterior caudal myotomes. A contrasting trend in gearing ratio was noted for frozen C. carpio (Rome and Sosnicki, 1991); however, measurements for these fish were made only for the epaxial region of muscle and so the varying fibre distribution at different regions along the length of the fish was not accounted for.

We propose that a quick and reliable method for predicting representative white muscle strain during fast-starts should involve data from high-speed films, equations 3, 4 and 6, and a gearing ratio based on the centroid of fibre area (similar to equation 9).

Fast-starts in six species of marine teleost involved waves of body bending travelling in a posterior direction along the fish’s spine (Wakeling and Johnston, 1998). The waves of bending were coupled to waves of muscle shortening and lengthening. The amplitude of the spine curvature increased towards the tail; however, the decreasing fish width resulted in a decrease in ε_red during starts. The fast-starts for the carp in the present study showed similar kinematic trends to those described previously for these marine fish.

The hydrodynamics of such fast-starts are similar to those for steady subcarangiform swimming, which also involve waves of bending which travel along the fish and increase in amplitude towards the tail (Gray, 1933; Bainbridge, 1963). Increases in the amplitudes of the lateral displacements towards the tail are a requirement for efficient motion (Lighthill, 1969). A large proportion of the hydrodynamic forces are delivered to the water in the caudal region during both steady swimming (Lighthill, 1970, 1971; Hess and Videler, 1984) and fast-starts (Weihs 1973; Webb, 1977; Frith and Blake, 1991).

Wakeling and Johnston (1998) discussed two possible effects of gearing ratio on white muscle strain for these starts. They proposed that, if the ratio decreased from a high value of 4 in the main body trunk to 2 in the caudal region, then the white muscle strain may remain reasonably constant in all myotomes. Alternatively, they suggested that, if the gearing ratio were constant throughout the length of the fish, then ε_w would show a decrease towards the caudal region, similar to the decrease in ε_red. Evidence from the present study (Fig. 5) suggests that the gearing ratio increases from approximately 2.0 in the region between 0.2L and 0.4L to a value of 2.6 at 0.7L. This situation is similar to the second case above in that there will be a decrease in ε_w along the fish, towards the tail. A decreased muscle strain and strain rate in the caudal region probably results in those fibres generating lower powers but having the potential to generate greater forces. Forces generated by the main myotomal muscle must be transmitted by structures in the caudal region to the tail blade, where a large proportion of the hydrodynamic work is done on the water both during fast-starts (Frith and Blake, 1991) and during steady swimming (for a review, see Wardle et al., 1995). The relative role of the skin, tendons and muscle in transmitting such forces is still not fully understood. However, force transmission requires these structures to be stiff and thus able to withstand high forces. It is likely that the increasing gearing ratio along a fish predisposes white muscle fibres to their different roles of power production in the main trunk and of force transmission in the caudal region.

This work was supported by a non-thematic grant (GR3/11028) from the Natural Environment Research Council of the UK.